The prediction sum of squares (PRESS) statistic assesses your model's predictive ability. PRESS, similar to the residual sum of squares, is the sum of squares of the prediction error. In PLS, Minitab only calculates PRESS if you cross-validated the model.
Minitab calculates PRESS in the following steps:
- Minitab recalculates the model as many times as there are observations, omitting a different observation each time. For each omitted observation, Minitab calculates the fitted or predicted response using the model.
- Minitab subtracts the predicted value from the observed response value. This is the true prediction error because the observation fit is independent of the model.
- Once Minitab conducts this routine for all observations, Minitab calculates PRESS using the formula:
In general, the smaller the PRESS value, the better the model's predictive ability. PRESS is used to calculate the predicted R2.
|yi||the observed response|
|the fitted response for the omitted observation|
|n||the number of observations|